Contributions to nonlinear system modelling and controller synthesis via convex structures

• Autores: Ruben Robles Ruiz
• Directores de la Tesis: Antonio Sala (dir. tes.), Miguel Ángel Bernal Reza (dir. tes.)
• Lectura: En la Universitat Politècnica de València ( España ) en 2018
• Idioma: español
• Tribunal Calificador de la Tesis: Teodoro Rafael Álamo Cantarero (presid.), Jesús Picó (secret.), Vicenç Puig (voc.)
• Programa de doctorado: Programa de Doctorado en Automática, Robótica e Informática Industrial por la Universitat Politècnica de València
• Materias:
  • Matemáticas
    • Análisis y análisis funcional
      • Convexidad, desigualdades
    • Análisis numérico
      • Matrices
    • Investigación operativa
      • Sistemas de control
      • Programación lineal
• Enlaces
  • Tesis en acceso abierto en: RiuNet
• Resumen

  • This thesis discusses different modelling methodologies to eke out best performance/stability results than conventional sector-nonlinearity Takagi-Sugeno (also known as quasi-LPV) systems modelling techniques are able to yield.

    Indeed, even if LMIs can prove various performance and stability bounds (decay rate, $\mathcal H_\infty$, etc.) for polytopic systems, it is well known that the proven performance depends on the chosen model and, given a nonlinear dynamic systems, the polytopic embeddings available for it are not unique. Thus, explorations on how to obtain the model which is less deletereous for performance are presented.

    As a last contribution, extending the polytopic Takagi-Sugeno setup to a gain-scheduled quasi-convex difference inclusion framework allows to improve the results over the polytopic models. Indeed, the non-scheduled convex difference inclusion framework was proposed by a research team in University of Seville (Fiacchini, Alamo, Camacho) as a generalised modelling methodology which included the polytopic one; this thesis poses a further generalised gain-scheduled version of some of these results.